The der likely has a model # stamped on the inner cage plate's back side, usually hard to see especially if there's corrosion or grime in the way. The important specs to duplicate is the tube clamp diameter (or E clip attachment), the large chain ring size capacity, the direction the cable pulls on the der from and the design of the parallelogram swing (which is top swing in this case). Otherwise there's a few grades of Shimano ders that should all work if the specs match. Andy

BTW- These Shimano ders, top swing MtBs, are well known for their slop in their pivots. We see most suffering form some amount of looseness but usually this isn't a performance factor of any great degree.